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Special automorphisms on Shimura curves and non-triviality of Heegner points

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Abstract

We define the notion of special automorphisms on Shimura curves. Using this notion, for a wild class of elliptic curves defined over Q, we get rank one quadratic twists by discriminants having any prescribed number of prime factors. Finally, as an application, we obtain some new results on Birch and Swinnerton-Dyer (BSD) conjecture for the rank one quadratic twists of the elliptic curve X 0(49).

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Correspondence to YongXiong Li.

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Cai, L., Li, Y. & Wang, Z. Special automorphisms on Shimura curves and non-triviality of Heegner points. Sci. China Math. 59, 1307–1326 (2016). https://doi.org/10.1007/s11425-016-5128-3

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  • DOI: https://doi.org/10.1007/s11425-016-5128-3

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